This paper studies the translation of proper names, particularly from English into Hungarian, within the frames of relevance theory. It is suggested that in translating a proper name translators have four basic operations at their disposal: transference, translation proper, substitution and modification. The paper presents two case studies, which attempt to explain the treatment of proper names in the Hungarian translations of Kurt Vonnegut's Slaughterhouse-Five and J. F. Cooper's The Last of the Mohicans. The analysis is based on the assumption that translation is a special form of communication, aimed at establishing interpretive resemblance between the source text and the target text, governed by the principle of optimal resemblance (Sperber and Wilson 1986; Gutt 1991). Proper names indeed seem to be translated in a predictable way: strategies are determined by considerations of how to preserve the semantic load of the proper names in the target communication situation.